Regular {p,q} tilings on the Poincaré disk model of hyperbolic space
Tiling {p, q}
Condition: (p-2)(q-2) > 4
✓ {5,4}: hyperbolic
ds² = 4(dx²+dy²)/(1-r²)²
The Poincaré disk is a model of hyperbolic geometry where geodesics are circular arcs perpendicular to the boundary. In a {p,q} tiling, every vertex has exactly q regular p-gons meeting.